Random Replacement Crisscross Butterfly Optimization Algorithm for Standard Evaluation of Overseas Chinese Associations

Abstract

The butterfly optimization algorithm (BOA) is a swarm intelligence optimization algorithm proposed in 2019 that simulates the foraging behavior of butterflies. Similarly, the BOA itself has certain shortcomings, such as a slow convergence speed and low solution accuracy. To cope with these problems, two strategies are introduced to improve the performance of BOA. One is the random replacement strategy, which involves replacing the position of the current solution with that of the optimal solution and is used to increase the convergence speed. The other is the crisscross search strategy, which is utilized to trade off the capability of exploration and exploitation in BOA to remove local dilemmas whenever possible. In this case, we propose a novel optimizer named the random replacement crisscross butterfly optimization algorithm (RCCBOA). In order to evaluate the performance of RCCBOA, comparative experiments are conducted with another nine advanced algorithms on the IEEE CEC2014 function test set. Furthermore, RCCBOA is combined with support vector machine (SVM) and feature selection (FS)—namely, RCCBOA-SVM-FS—to attain a standardized construction model of overseas Chinese associations. It is found that the reasonableness of bylaws; the regularity of general meetings; and the right to elect, be elected, and vote are of importance to the planning and standardization of Chinese associations. Compared with other machine learning methods, the RCCBOA-SVM-FS model has an up to 95% accuracy when dealing with the normative prediction problem of overseas Chinese associations. Therefore, the constructed model is helpful for guiding the orderly and healthy development of overseas Chinese associations.

1. Introduction

As an important organizational form of overseas Chinese society and a direct participant and promoter of the great rejuvenation of China, the Overseas Chinese Association has shown a good development momentum in the new era. In recent years, Zhejiang overseas Chinese groups have gradually increased in number and expanded in scale. However, most overseas Chinese associations are still irregular in terms of their establishment, operation, and management, meaning that they cannot become exemplary and representative featured overseas Chinese associations. The problems of irregularities in overseas Chinese associations are mainly manifested in ten aspects: legality, incomplete constitutions, irregular elections, the phenomenon of the “one-man meeting”, prominent concurrent roles, unsound teams, significantly bad records held by the head of the association, lack of innovation awareness caused by aging, the existence of zombie groups, and a lack of professionalism. Both internal contradictions and external pressures lead to the emergence of these problems, which hinder the development of the overseas Chinese associations and undermine their harmonious atmosphere. Carrying out the standardization of overseas Chinese associations is a necessary and urgent task in order to safeguard the rights and interests of overseas Chinese citizens. Therefore, it is necessary to conduct an in-depth analysis of the factors affecting the standardized construction of overseas Chinese associations and establish an evaluation model to help guide their orderly and healthy development.

The study of overseas Chinese associations has been a hot topic in academic circles. Many scholars have studied the development of overseas Chinese associations around the world from multiple perspectives. Li et al. [1] studied the reasons, characteristics, and influence of explosive growth of overseas Chinese associations in Europe from the 1980s to the 1990s. Fei et al. [2] studied how “new” overseas Chinese immigrant associations drive the development of “old” overseas Chinese immigrant associations in the Pacific region from a historical perspective. Maurice et al. [3] focused on how the Chinese immigrants and overseas Chinese associations in Singapore adapted to colonial society in the 19th century. Ma et al. [4] elaborated on the formation of overseas Chinese associations in the United States and their influence on local politics and economy. The above scholars have studied overseas Chinese associations from the perspectives of history, politics, and international relations, but no scholars have automated their analysis by means of computer algorithms yet [5]. Previously, research has only been conducted to classify non-profit organizations by their fields of activity through computer algorithms. In this paper, we will use intelligent algorithms to calculate 1050 valid questionnaires made by overseas Chinese of Zhejiang nationality from all over the world and establish a program that can quickly identify the regularity of overseas Chinese associations so as to provide a reference allowing Chinese embassies and consulates abroad to accurately grasp the latest trends of overseas Chinese associations and examine whether or not they are legitimate. This procedure can provide a standard for the standardization of overseas Chinese associations, so that the rights and interests of every overseas Chinese can be protected and avoid irregular overseas Chinese associations from harming the rights and interests of them.

Based on existing data, this paper first proposes RCCBOA with SVM, the core of which is mainly combined with random replacement and a crisscross search strategy to better predict the standardized construction of overseas Chinese associations, effectively boosting the accuracy of the solution of BOA. BOA is one of many intelligent optimization algorithms. It is a global optimization algorithm inspired by butterfly foraging behavior that was proposed by Sankalap Arora and Satvir Singh in 2019 [6]. BOA has a simple structure, few parameters, and is based on a novel idea; it is suitable for solving high-dimensional optimization problems. Compared with other optimization algorithms proposed recently, the optimization performance is stronger and the influence of dimensional changes is smaller, so it has relevant research potential. However, BOA has the problems of a slow convergence speed and low solution accuracy on some benchmark functions. According to “no free lunch” (NFL) theorems [7], no one algorithm can be applied to all problems. Similarly, the main reason why we conducted this research was to find a type of benchmark problem or practical problem that would be suitable for the algorithm. The relevant work on BOA has attracted a wide range of scholars both at home and abroad. Long et al. [8] designed an enhanced adaptable BOA (EABOA) to improve the parameter estimation of PV models; this was also tested on 12 classical benchmark function sets to verify its superior performance. Sharma et al. [9] proposed a boosted BOA with bidirectional search (BBOA) and tested it on seven unimodal benchmark functions and three practical engineering optimization problems. Mortazavi et al. [10] used a fuzzy BOA (FBOA) and tested it on resolving certain constrained and non-constrained optimization problems. Sundaravadivel et al. [11] proposed a weighted BOA (WBOA) with an intuitionistic fuzzy gaussian function to predict the outcome of infection with COVID-19. Zhou et al. [12] proposed an improved BOA to apply numerical examples of a simply-supported beam and truss structure. Thawkar et al. [13] introduced an ant lion optimizer into BOA (BOAALO), which was used to predict the benign or malignant status of breast tissue. Long et al. [14] designed a hybrid BOA with an adaptive gbest-guided search strategy and pinhole-imaging-based learning (PIL-BOA) to deal with feature selection problems. Sowjanya et al. [15] utilized BOA and gas Brownian motion optimization to obtain the optimal threshold levels for image segmentation. Some other improved algorithms have also been widely used to solve complex problems in various fields. Descriptions of the novel improved algorithms are provided in

Table 1. Description of other novel improved algorithms.

Author	Year	Proposed Algorithm	Description
Hu et al. [16]	2021	An improved Harris hawk optimization (HHOSRL)	It was applied to feature selection and gained a high accuracy.
Fan et al. [17]	2021	A new particle swarm optimization (PSOCS)	It was used to estimate the parameters of PV models.
Shi et al. [18]	2021	An enhanced colony predation algorithm (ECPA)	It used a kernel extreme learning machine to classify the severity of COVID-19.
Zhou et al. [19]	2021	A novel enhanced spherical evolution algorithm (DSCSE)	It was applied to evaluate unknown parameters of PV models.
Yu et al. [20]	2021	An improved slime mould algorithm (WQSMA)	It provided effective assistance in solving optimization problems.
Zhou et al. [21]	2021	A new gradient-based optimizer with random learning mechanism (RLGBO)	It was employed to gain the PV model parameters of different conditions.
Xu et al. [22]	2021	An innovative binary version of moth-flame optimizer (ESAMFO)	It was utilized to select optimal feature subsets with the K-Nearest Neighbor Classifier.
Liu et al. [23]	2021	A novel ant colony optimizer (CLACO)	It was verified by comparison with certain excellent peers.
Zhao et al. [24]	2021	An improved salp swarm algorithm (EHSSA)	It was tested on CEC2014 functions and image segmentation problems.
Yu et al. [25]	2020	A dynamic bare-bones fruit fly optimization algorithm (BareFOA)	It was tested on with CEC2017 and seven engineering optimization problems.
Chen et al. [26]	2020	An enhanced DE-driven multi-population Harris hawks optimization (CMDHHO)	It was compared with plenty of other algorithms based on CEC2017 and CEC2011.
Chen et al. [27]	2020	A boosted sine cosine algorithm (OMGSCA)	It was applied in CEC2014 and used to solve some real-world optimization problems.
Tu et al. [28]	2019	An adaptive support vector machine framework (RF-CSCA-SVM)	It was regarded as being successful for predicting student graduation.
Chen et al. [29]	2019	A hybrid whale optimization algorithm (BWOA)	It was treated as an effective means to solve complex problems.

.

Aiming at addressing the deficiencies of BOA, we propose an improved butterfly algorithm combining random replacement and a crisscross search strategy. The combination of these two strategies effectively boosts the performance of the original one, enabling it to have a better performance on complex problems. In order to evaluate the performance of the proposed algorithm, it is compared with nine recently proposed advanced algorithms on the CEC 2014 benchmark test set, including CDLOBA [30], CBA [31], RCBA J [32], MWOA [33], LWOA [34], IWOA [35], CEFOA [36], CIFOA [37], and AMFOA [38]. In addition, RCCBOA was also combined with SVM to solve the problem of predicting the standardized construction of overseas Chinese associations. Experimental results show that the convergence speed and convergence accuracy of this algorithm are better than those of other advanced algorithms, and the best SVM optimized by RCCBOA had an accuracy rate of 95% on the relevant data set. Therefore, the proposed RCCBOA has very broad application prospects. The main contributions of this paper are as follows:

• A new type of enhanced BOA which combines a random replacement strategy and cross search strategy is proposed.
• RCCBOA is compared with nine other advanced algorithms on the CEC 2014 benchmark function test.
• RCCBOA is combined with SVM to solve the problem of predicting overseas Chinese associations.

The organizational structure of the thesis is as follows. Section 2 describes the SVM and BOA. Section 3 and Section 4 introduce the proposed RCCBOA and RCCBOA-SVM. Section 5 describes the data sources and experimental settings used. Section 6 shows the experimental results. Section 7 discusses the experimental results, and the last section summarizes the full paper and related future prospects.

2. Backgrounds

2.1. Overseas Chinese Associations

The full name of “Qiao Tuan” is “Overseas Chinese Association”. It is a formal group made up of overseas Chinese nationals due to their certain related attributes and is an important organizational form of overseas Chinese society, whose related attributes include factors such as living area, work industry, academic field, language exchange, ethnic blood relationship, etc. At present, the number of overseas Chinese associations exceeds 25,700. Overseas Chinese associations have the functions of economic construction, safeguarding rights and interests, overseas friendship, political participation, cultural dissemination, and public welfare dedication. Overseas Chinese groups have participated in China’s economic construction for a long time to achieve mutual benefits, contributing to the masses and earnestly safeguard the basic rights and interests of overseas Chinese. Moreover, overseas Chinese associations organize networking activities for overseas Chinese nationals to promote communication and interaction among overseas Chinese people; they pay attention to political changes, keep abreast of current trends, strive for resources, and serve overseas Chinese nationals. Overseas Chinese associations are an important part of the overseas dissemination of Chinese culture, inheriting culture vertically and spreading culture horizontally. Moreover, overseas Chinese associations are parts of the country where they are located, and it is the basic responsibility of the overseas Chinese associations to serve local society and participate in public welfare matters.

Overseas Chinese associations are known as one of the three pillars of overseas Chinese society and an important organizational form for maintaining its orderly operation. Overseas Chinese associations have functions such as safeguarding the rights and interests of overseas Chinese, building overseas friendships, promoting cultural dissemination, and contributing to public welfare. Currently, the number of overseas Chinese nationals exceeds 60 million, and the number of overseas Chinese associations around the world has reached 25,700. The total number of overseas Chinese nationals from Zhejiang Province is 3.792 million, ranking fifth in the country. There are also a large number of overseas Chinese associations composed mostly of Zhejiang nationals. According to incomplete statistics, there are 865 overseas Chinese associations, which are mainly distributed in 66 countries including Italy, Spain, the United States, and Australia.

2.2. Butterfly Optimization Algorithm (BOA)

In recent years, many optimization algorithms have been proposed for solving approximate optimal problems, such as hunger games search (HGS) [39], Harris hawks optimization (HHO) [40], the slime mould algorithm (SMA) [41], the Runge–Kutta optimizer (RUN) [42], the colony predation algorithm (CPA) [43], and the weighted mean of vectors (INFO) [44].

These algorithms have a strong search ability and can solve many practical problems, with applications such as medical diagnosis [45,46], economic emission dispatch problems [47], engineering design [48,49,50], parameter tunning for machine learning models [18,51,52], image segmentation [53,54,55], plant disease recognition [56], feature selection [57,58], bankruptcy prediction [59,60], prediction problems in the educational field [61,62], PID optimization control [63,64], the detection of foreign fibers in cotton [65,66], expensive optimization problems [67,68], multi-objective or many optimization problems [69,70,71], the fault diagnosis of rolling bearings [72,73], gate resource allocation [74,75], combination optimization problems [76], big data optimization problems [77], green supplier selection [78], and scheduling problems [79,80].

BOA [6] is a newly proposed optimization algorithm which is based on imitating the foraging behavior of butterflies in nature [6]. Since its introduction, it has been applied to many problems, such as fault diagnosis [81] and disease diagnosis [82]. Each butterfly acts as a search operator and performs an optimization process in the search space. The butterfly can perceive and distinguish different fragrance intensities, and the fragrance emitted by each butterfly has a certain level of intensity. One must assume that the intensity of the fragrance produced by the butterfly is related to its fitness; when the butterfly moves from one place to another, its fitness will also change accordingly. The scent emitted by the butterfly will spread in the air and be felt by other butterflies. This is the process by which individual butterflies share personal information with other individual butterflies, thus forming a collective social knowledge network. When a butterfly detects the scent of other butterflies, it will move to the butterfly with the most scent, which is called a global search. Conversely, when a butterfly cannot perceive the fragrance of other butterflies, it will move randomly, which is called a local search.

If $X_i=\left(x_{i1},x_{i2},\dots ,x_{iD}\right)$ is the $i$-th ($i=1,2,\dots ,N$) butterfly individual, D is the search space dimension, N is the butterfly population size, and the position update of the butterfly individual is as shown in Equation (1).

$$x_i^{t+1}=\{\begin{array}{c}{x}_i^t+\left(r^2\times g^{\ast }-x_i^t\right)f_i\\ x_i^t+\left(r^2\times x_j^t-x_k^t\right)f_i\end{array}$$

(1)

where $x_i^{t+1}$ is the solution vector of the $i$-th butterfly in $t+1$ iterations; $r$ is a random number between 0 and 1; $g^{\ast }$ represents the global optimal individual in the current iteration; and $x_i^t$ and $x_i^t$ are randomly generated butterfly individuals, representing the solution vector of the $j$-th butterfly and the $k$-th butterfly in the solution space. The fragrance emitted by the $i$-th butterfly is denoted by $f_i$, and the specific expression of $f_i$ is shown in Equation (2).

$$f=c{I}^a$$

(2)

where $f$ is the level of fragrance perception, $c$ is the form of perception, and $a$ is the power exponent, which depends on the form of perception, reflecting the different degrees of scent absorption.

The BOA is divided into three stages; the pseudo-code is shown in Algorithm 1.

(1)

Initial stage. The parameter values used in BOA are assigned, and when these values are set the algorithm proceeds to create an initial butterfly population for optimization. The positions of the butterflies are randomly generated in the search space and their scent and fitness values are calculated and stored.

(2)

Iterative stage. In each iteration, all butterflies in the solution space are moved to new positions and their fitness values are re-evaluated. The algorithm m first calculates the fitness values of all butterflies at different positions of the solution space. Then, these butterflies will use Equation (1) to generate fragrance in their place.

(3)

End stage. Iteration continues until the maximum number of iterations is reached. When the iteration phase ends, the algorithm outputs the optimal solution with the best fitness.

Algorithm 1: Pseudo-code of BOA.

Initialize population number $n$, dimensions $d$, max evaluations $Ma{x}_{FEs}$, objective function $f\left(x\right);$ Initialize sensor modality $c$, power exponent $a$, switch probability $p,$ and evaluations $t$; Initialize the population of butterflies $x_i \left(i=1,2,\dots ,n\right)$; Gain intensity $I_i$ by $f\left(x_i\right)$; While ($t\le Ma{x}_{FEs}$): Calculate the fragrance $bf$ of each butterfly using Equation (2); Gain the best $bf$; For $i=1 to n$ Update $r \mathrm{in} \left[0, 1\right];$     If $r$ < $p$       Move to the best solution with Equation (1);     Else       Move randomly using Equation (1);     End if   End for   $t$ = $t$ + 1; Update parameter $a$; End while Output best solution.

2.3. Support Vector Machine

The purpose of the support vector machine (SVM) is to find the hyperplane that is the furthest away from various sample points. SVM is a supervised learning method used for classification problems, with the goal of finding the hyperplane that can most accurately separate positive and negative samples. Assuming given sample data $\mathrm{G}=\left(x_i,y_i\right),i=1,\dots ,N,x\in R^d,y\in \left\{\pm 1\right\}$, the hyperplane is expressed as follows:

$$\mathrm{g}\left(x\right)={\omega }^{\mathrm{T}}x+b$$

(3)

The SVM model according to the existing standard is as follows:

$$\{\begin{array}{c}\min \left(\omega \right)=\frac{1}{2}{\omega }^2+c{\displaystyle \sum _{i=1}^N}{{\xi }_i}^2\\ s.t y_i\left({\omega }^{\mathsf{{\rm T}}}{x}_i+b\right)\ge 1-{\xi }_i,i=1,2,\dots ,N\end{array}$$

(4)

where $\omega$ is the inertia weight, $b$ is a constant, ${\xi }_i$ is a slack variable, and $c$ is a disciplinary factor.

The initial low-dimensional sample set is mapped to a high-dimensional space H by introducing a kernel function; then, the optimal classification surface is established using a linear method. The conversion formula is shown below.

$$\{\begin{array}{c}Q\left(\alpha \right)=\frac{1}{2}{\displaystyle \sum _{i=1}^N}{\alpha }_i{\alpha }_j{y}_i{y}_{j}k\left(x_i,x_j\right)-{\displaystyle \sum _{i=1}^N}{\alpha }_i\\ s.t {\displaystyle \sum _{i=1}^N}{a}_i{y}_i=0,0\le a_i\le C,i=1,2, \dots ,N\end{array}$$

(5)

where ${\alpha }_i$ is the Lagrange multiplier and $k\left(x_i,x_j\right)$ is the kernel function, which can be expressed in Equation (6).

$$k\left(x,y\right)=e^{-\gamma \Vert x_i-x_j\Vert }$$

(6)

where $\gamma$ is a kernel parameter, which represents the interaction width of the kernel function.

3. Suggested RCCBOA

3.1. Random Replacement Strategy

Most optimization algorithms will show global exploration behavior in the early stage [83]. When the algorithm exploration is weak, the convergence speed will be slow and it will be easy to fall into the local optimum [84]. Thus, we introduce a random replacement strategy to BOA, which effectively helps the individuals of the population to move closer to the food source, thereby improving the algorithm’s convergence speed. The individuals of the population are compatible with the optimal individual in some dimensions, and it is possible that some of the dimensions of the individual will deviate from those of the optimal individual. In this case, the current position is replaced with the position of the optimal solution with some probability. The probability value is mainly determined by comparing the ratio of the remaining time of the algorithm to the total running time and the Cauchy random number. The random replacement strategy can easily be replaced in the early stage of the algorithm, and it is less likely to be replaced in the later stage. In short, the random replacement strategy can effectively improve the convergence speed of the algorithm and prevent the algorithm from falling into the local optimum prematurely.

3.2. Crisscross Search

The crisscross search strategy is derived from the crisscross optimization algorithm (CSO) proposed by Meng et al. in 2014 [85], which includes vertical crossover and horizontal crossover. Its effectiveness has been demonstrated in many optimization algorithms [86]; for example, Zhao et al. [87] used it in ant colony optimization to solve the problem of multi-threshold image segmentation. Liu et al. [88] designed an improved Harris hawks optimizer (HHO) with the crisscross search strategy to estimate the parameters of PV models.

3.2.1. Vertical Crossover Search

The function of vertical crossover is mainly to increase the diversity of the population to avoid it falling into a stagnant state; it mainly uses two dimensions to achieve crossover. Assuming that the $j1$th and $j2$th dimensions of the $i$-th individual are selected and that a vertical crossover operation is then performed, the new offspring $Mv{c}_i$ can be obtained by Equations (7) and (8).

$$Mv{c}_{i,j1}=r\times M_{i,j1}+\left(1-r\right)\times M_{i,j2}$$

(7)

$$r=unifrnd\left(0,1\right)$$

(8)

where $i$ = $1,2,\dots ,N$; $j1,j2=1,2,\dots ,D$; $M_{i,j1}$ represent the $j1$ and $j2$ dimensions of the $i$ agent $M_i.$ Additionally, $r$ is a random number uniformly distributed from 0 to 1. Special attention must be paid to the normalization of the lower and upper bounds of each dimension to ensure that the individual remains within the bounds after the operation before implementing the vertical crossover operation. After performing vertical crossing, a reverse normalization operation needs to be performed to ensure that the offspring is still within the given boundary.

3.2.2. Horizontal Crossover Search

Horizontal crossover can further improve the search and development of algorithms. It mainly involves crossover operations being performed on all dimensions of two different agents. Assuming that the agents $M_{i1}$ and $M_{i2}$ are selected to perform level crossing, the new agents $Mh{c}_{i1}$ and $Mh{c}_{i2}$ can be obtained using Equations (9) and (10).

$$Mh{c}_{i1,j}=r_1\times M_{i1,j}+\left(1-r1\right)\times M_{i2,j}+c1\times \left(M_{i1,j}-M_{i2,j}\right)$$

(9)

$$Mh{c}_{i2,j}=r_2\times M_{i2,j}+\left(1-r1\right)\times M_{i1,j}+c2\times \left(M_{i2,j}-M_{i1,j}\right)$$

(10)

where $Mh{c}_{i1,j}$ and $Mh{c}_{i2,j}$ are $j$-th dimension of $Mh{c}_{i1}$ and $Mh{c}_{i2}$; $M_{i1,j}$ and $M_{i2,j}$ is the $j$-th dimension of $M_{i1}$ and $M_{i2}$; and $r_1$ and $r_2$ are uniformly distributed random numbers from 0 to 1. $c1$ and $c2$ are uniformly distributed random numbers in [−1, 1].

3.3. Proposed RCCBOA

The idea of the RCCBOA is to introduce random replacement and crossover strategies on the basis of the BOA. Regarding the early exploration and later development of the algorithm, it can be determined by including the ratio of the current number of iterations to the total number of iterations. In the exploration phase, the random replacement strategy uses the location of the optimal solution to replace the current solution, which can improve the convergence speed of the BOA. In the exploitation stage, a cross-search strategy is introduced to improve the exploration and exploitation capabilities of the original algorithm, which makes it possible get rid of the local optimal solution as much as possible. The effective combination of the two greatly improves the performance of the original BOA. The pseudo-code of the RCCBOA is shown in Algorithm 2. Based on the BOA, random replacement and crisscross search mechanisms are mainly used in the second stage of the BOA. At the beginning of each iteration, a random replacement mechanism is used to replace the current position with the position of the optimal solution with a certain probability and then evaluate it. At the end of each iteration, the population is updated and evaluated again using the crisscross search mechanism. For a better view, the flowchart of the RCCBOA is offered in Figure 1.

Algorithm 2: Pseudo-code of the RCCBOA.

Initialize population number $n$, dimensions $d$, max evaluations $Max\_FEs$, objective function $f\left(x\right);$ Initialize sensor modality $c$, power exponent $a$, switch probability $p$ and evaluations $t$; Initialize the population of butterflies $x_i \left(i=1,2,\dots ,n\right)$; Gain intensity $I_i$ by $f\left(x_i\right)$ While ($t\le Max\_FEs$) Calculate the fragrance $bf$ of each butterfly using Equation (2); Gain the best $bf$; Gain butterfly individuals by the random replacement strategy; Update the best solution and position; For $i=1 to n$ Update $r \mathrm{in} \left[0,1\right];$     If $r$ < $p$       Move to the best solution using Equation (1);     Else       Move randomly using Equation (1);     End if   End for   Update the population of butterflies using Equations (9) and (10);   $t$ = $t$ + 1; Update parameter $a$; End while Output best solution;

4. Proposed RCCBOA-SVM Method

Firstly, we subject the proposed RCCBOA to data-level feature selection, aiming to obtain effective features in the dataset. Secondly, it is used to optimize the penalty factor C and kernel parameter γ of the SVM. The framework of RCCBOA-SVM is shown in Figure 2. Finally, the model mainly includes two important components in the left half for feature selection and uses the RCCBOA to optimize the two parameters $C$ and $\gamma$ in the SVM model. In the right half, the best model obtains the classification accuracy (ACC) through 10-fold cross-validation.

For feature selection problems, the focus of the algorithm is to select or not to select a certain feature in the dataset, thus maximizing the classification accuracy of the most effective feature. RCCBOA is inconsistent with the two-dimensionality required by the feature selection problem when solving the problem, and these algorithms cannot be used to directly solve the feature selection problem. Therefore, it is necessary to convert each solution vector in this algorithm to binary form through the sigmoid transfer function, which consists of only ‘0’ and ‘1’. To achieve this transformation, an S-shaped transformation function is used, which gives the probability of selecting a particular feature in the solution vector.

Through feature selection, the minimum number of key features can be successfully obtained. However, the fitting accuracy of the SVM depends on the values of the parameters ($C$, $\gamma$), and different parameters are suitable for different sample data sets. Therefore, it is necessary to further optimize the SVM parameters using RCCBOA to achieve the optimal effect.

5. Experiments

5.1. Collection of Data

The data involved in this paper were mainly obtained from overseas Chinese citizens; 1050 people were selected as the research objects. The 28 attributes of the test subjects were gender; age range; location of hometown; current identity; place of birth; when they went abroad; reason for going abroad; in which year they became permanent residents in their country of residence; highest level of education (degree); major; type of work currently engaged in; whether they had relatives living together in their native country; their position held in their native country; whether they had joined an overseas Chinese association; whether they were a founder of an overseas Chinese association; their reason for founding an overseas Chinese association; their motivation for joining an overseas Chinese association; their position held in the overseas Chinese association; whether their overseas Chinese association had a clear division of duties; whether their overseas Chinese association is harmonious; whether their overseas Chinese association is a non-profit organization; whether the charter of the overseas Chinese association is reasonable; whether the overseas Chinese association holds regular meetings; whether every member of the association has the right to vote and be elected; whether every member of the association has the right to criticize, make suggestions, and supervise the overseas Chinese association; whether the membership fee of the association is paid according to the regulations; the main source of funding for the overseas Chinese association; and, lastly, their expectations and suggestions for the overseas Chinese association. The importance of these 28 attributes and their internal connections were explored, and based on this a model was built.

Table 2. Description of the 28 attributes.

Attributes	Name	Description
A1	Gender	Male—1; Female—0
A2	Age range	0–30 years old—1; 30–60 years old—2; 60–80 years old—3.
A3	Location of hometown	Wenzhou—1; Lishui—2; other places—3.
A4	Current identity	Overseas Chinese with Chinese nationality or international students—1; descendants of overseas Chinese who were born in the country of residence and obtained the nationality of the residence country—2; returned overseas Chinese and family members of returned overseas Chinese—3.
A5	Place of birth	China (Hong Kong, China)—1; foreign countries—2; unable to confirm—0.
A6	When they went abroad	Before 1949—1; between 1950 and 1978—2; 1979 till now—3.
A7	Reasons for going abroad	Family visit—1; work, trade, or investment—2; studying abroad or skilled immigrants—3; other reasons or no reasons—4.
A8	In which year they became permanent residents	Before 2000—1; 2000 till now—2; no permanent residence—0
A9	Highest level of education (degree)	High school/technical secondary school/secondary vocational school/technical school or below—1; junior college/higher vocational college—2; Bachelor degree or above—3.
A10	Major	Liberal arts—1; science—2; others (catering, party school cadre training, entertainment, tourism, army academy)—3; none or unknown—0
A11	Type of work currently engaged in	worker, trade, business and investment—1; research and development, knowledge or education—2; catering—3; other or none—4.
A12	Relatives living together in China	Immediate family member—1; non-immediate relatives—2; both 1 and 2–3; none—0.
A13	Their position held in China	National level—1; provincial level—2; city/county level—3; other or none—0.
A14	Whether they had joined an overseas Chinese association	Yes—1; no—0.
A15	Whether they had acted as the founder of an overseas Chinese association	Yes—1; no—0.
A16	Reason for founding the overseas Chinese association	Business relations—1; geographical relations—2; learning relations—3; other reasons or none—4.
A17	Motivation for joining the overseas Chinese association	Active—1; passive (invited by friends)—2; other or skip—3.
A18	Position held in the overseas Chinese association	Positive—1; deputy—2; others—3; none—0.
A19	Whether the overseas Chinese association has a clear division of duties	Yes—1; none or other—0.
A20	Whether the overseas Chinese association is harmonious	Harmony—1; so-so or unknown—2; skip—0.
A21	Whether the overseas Chinese association is a non-profit organization	Yes—1; no—2; unknown or skip—0.
A22	Whether the charter of the overseas Chinese association is reasonable	Yes—1; none—0.
A23	Whether the overseas Chinese association holds regular meetings	Yes—1; no—0.
A24	Whether every member of the association has the right to vote and be elected	Yes—1; no—0.
A25	Whether every member of the association has the right to criticize, make suggestions, and supervise the overseas Chinese association	Yes—1; no—0.
A26	Whether the membership fee of the association is paid according to the regulations	Yes—1; no—0.
A27	Main source of funding for the overseas Chinese association	Other fixed income—1; membership fees (including membership fees and donation)—2; no dues, only donations—3; unknown or other—0.
A28	Expectations and suggestions for the overseas Chinese association	Positive—1; so-so or no (skip)—2; negative—3.

details the 28 attributes.

Among these, whether the overseas Chinese group/association is standardized is considered among the 28 attributes (attribute A17 (motivation of joining the overseas Chinese association), A19 (whether the overseas Chinese association has a clear division of duties), A21 (whether the overseas Chinese association is a non-profit organization), A22 (whether the charter of the overseas Chinese association is reasonable), A23 (whether the overseas Chinese association holds regular meetings), A24 (whether every member of the association has the right to vote and be elected)) are the basis of determining whether the overseas Chinese association is standard.

5.2. Experimental Setup

Ensuring the independence of experimental procedures is extremely important, as in computational science and molecular characterization [89,90], location-based services [91,92], drug discovery [93,94], pharmacoinformatic data mining [95,96], and information retrieval services [97,98,99]. The comparison test described in this section was carried out on a computer with a main central processing unit (CPU) frequency of 3.4 GHz and the win10 operating system (Microsoft, Redmond, WA, USA). Simulation experiments were performed in MATLAB R2016a (MathWorks, Natick, MA, USA). In benchmarking experiments, each comparison algorithm ran 30 experiments simultaneously. When dealing with classification problems, the data were scaled to [−1,1]. $k$-fold cross-validation (CV) was used to split the data, where $k$ was set to 10.

6. Experimental Results

6.1. Benchmark Function Validation

We mainly conducted test experiments using RCCBOA on the CEC2014 benchmark function set, including mechanism combination experiments and comparative experiments with existing advanced algorithms. Detailed information about the CEC2014 benchmark set can be found in Appendix A (see

Table A1. Summary of the CEC2014 benchmark problem [120].

Type	No.	Function	Optimum Value
Unimodal Functions	1	Rotated High Conditioned Elliptic Function	$f_1\left\{X_{min}\right\}=100$
	2	Rotated Bent Cigar Function	$f_2\left\{X_{min}\right\}=200$
	3	Rotated Discus Function	$f_3\left\{X_{min}\right\}=300$
Multimodal Functions	4	Shifted and Rotated Rosenbrock’s Function	$f_4\left\{X_{min}\right\}=400$
	5	Shifted and Rotated Ackley’s Function	$f_5\left\{X_{min}\right\}=500$
	6	Shifted and Rotated Weierstrass Function Function	$f_6\left\{X_{min}\right\}=600$
	7	Shifted and Rotated Griewank’s Function	$f_7\left\{X_{min}\right\}=700$
	8	Shifted Rastrigin’s Function	$f_8\left\{X_{min}\right\}=800$
	9	Shifted and Rotated Rastrigin’s Function	$f_9\left\{X_{min}\right\}=900$
	10	Shifted Schwefel’s Function	$f_{10}\left\{X_{min}\right\}=1000$
Hybrid Functions	11	Shifted and Rotated Schwefel’s Function	$f_{11}\left\{X_{min}\right\}=1100$
	12	Shifted and Rotated Katsuura Function	$f_{12}\left\{X_{min}\right\}=1200$
	13	Shifted and Rotated Happycat Function	$f_{13}\left\{X_{min}\right\}=1300$
	14	Shifted and Rotated Hgbat Function	$f_{14}\left\{X_{min}\right\}=1400$
	15	Shifted and Rotated Expanded Griewank’s Plus Rosenbrock’s Function	$f_{15}\left\{X_{min}\right\}=1500$
	16	Shifted and Rotated Expanded Scaffer’s Function	$f_{16}\left\{X_{min}\right\}=1600$
	17	Hybrid Function 1 (N = 3)	$f_{17}\left\{X_{min}\right\}=1700$
	18	Hybrid Function 2 (N = 3)	$f_{18}\left\{X_{min}\right\}=1800$
	19	Hybrid Function 3 (N = 4)	$f_{19}\left\{X_{min}\right\}=1900$
	20	Hybrid Function 4 (N = 4)	$f_{20}\left\{X_{min}\right\}=2000$
Composition Functions	21	Hybrid Function 5 (N = 5)	$f_{21}\left\{X_{min}\right\}=2100$
	22	Hybrid Function 6 (N = 5)	$f_{22}\left\{X_{min}\right\}=2200$
	23	Composition Function 1 (N = 5)	$f_{23}\left\{X_{min}\right\}=2300$
	24	Composition Function 2 (N = 3)	$f_{24}\left\{X_{min}\right\}=2400$
	25	Composition Function 3 (N = 3)	$f_{25}\left\{X_{min}\right\}=2500$
	26	Composition Function 4 (N = 5)	$f_{26}\left\{X_{min}\right\}=2600$
	27	Composition Function 5 (N = 5)	$f_{27}\left\{X_{min}\right\}=2700$
	28	Composition Function 6 (N = 5)	$f_{28}\left\{X_{min}\right\}=2800$
	29	Composition Function 7 (N = 3)	$f_{29}\left\{X_{min}\right\}=2900$
	30	Composition Function 8 (N = 3)	$f_{30}\left\{X_{min}\right\}=3000$

), coming from congress on evolutionary computation of the world’s highest conference. The experimental results obtained from 30 independent repeated experiments under the same conditions were analyzed, including the average and standard results obtained by the algorithm on each benchmark function. We used the Wilcoxon signed-rank test non-parametric statistical test and the Friedman test, which have used in many other works, to estimate the performance [100,101,102,103,104].

6.1.1. The Component Foundation

To assess the contribution of random replacement and horizontal crossover search mechanisms to the original BOA, a mechanism combination experiment was conducted. By randomly combining the two mechanisms, three additional algorithms were developed—namely, RCCBOA, RBOA, and CCBOA. As shown in

Table 3. Four BOA variants with two strategies.

Algorithms	R	CC
RCCBOA	1	1
CCBOA	0	1
RBOA	1	0
BOA	0	0

, where “R” and “CC” represent the random replacement strategy and the crossover strategy, respectively, “1” indicates that the BOA incorporates the policy and “0” indicates that the BOA does not incorporate the policy. For example, RCCBOA means that the BOA combines both the random replacement strategy and the horizontal crossover search strategy. Each algorithm was tested on the CEC 2014 benchmark function test set. The experimental results are shown in

Table 4. Average ranking of four BOA variants.

Algorithm	Rank	ARV
RCCBOA	1	1.426667
CCBOA	2	1.704444
RBOA	3	2.908889
BOA	4	3.96

. For fair comparison, the parameters commonly used in the experiment were not set to 30. In addition, we utilized the Wilcoxon signed-rank test and average value (ARV) to examine the average ranking values of the algorithms involved to further investigate the difference between the two. It can be seen that the average performance of the RCCBOA combining both strategies was the best.

To further visualize the performance of RCCBOA, Figure 3 shows the convergence curves of RCCBOA, CCBOA, RBOA, and BOA on F3, F7, F11, F13, F16, F20, F23, F27, and F29. Obviously, RCCBOA had a faster convergence speed and smaller convergence value on these benchmark functions than on the other algorithms. In conclusion, the BOA performance achieved by combining both the random replacement strategy and the horizontal crossover search strategy was the best.

6.1.2. Comparison with Advanced Methods

To evaluate the superiority of the RCCBOA algorithm, this section compares the RCCBOA algorithm with nine improved optimization algorithms, including CDLOBA [30], CBA [31], RCBA J [32], MWOA [33], LWOA [34], IWOA [35], CEFOA [36], CIFOA [37], and AMFOA [38]. These nine advanced algorithms are improved compared to classic algorithms and have strong optimization abilities. We chose to use the CEC 2014 benchmark function as the test set and set the search agent to 30, the dimension to 30, and the maximum number of evaluations to 300,000. In addition, each algorithm was run separately for 30 experiments to obtain the average value; the parameter settings are shown in

Table 5. Parameters setting of the RCCBOA and other algorithms.

Method	Parameter
RCCBOA	$p=0.8$
CDLOBA	$r=\left[1,30\right]$$; Q_{min}=0$$;Q_{max}=2$
CBA	$p=\left[0,1\right]$$; Q_{min}=0$$;Q_{max}=2$
RCBA	$A=\left[0,1\right];r=0.5;Q_{min}=0$$;Q_{max}=2$
MWOA	$a_1=\left[0,2\right];a_2=\left[-2,-1\right]$
LWOA	$a_1=\left[0,2\right];a_2=\left[-2,-1\right];b=1$
IWOA	$a_1=\left[0,2\right];a_2=\left[-2,-1\right];b=1;C_r=0.1$
CEFOA	$initiallocation ϵ\left[-10,10\right]$
CIFOA	$mr=0.8$
AMFOA	${\sigma }_1=0;{\sigma }_2=0$

.

Table 6. Comparison of the results of the RCCBOA and different advanced algorithms.

Fuctions	Indicators	RCCBOA	CDLOBA	CBA	RCBA	MWOA	LWOA	IWOA	CEFOA	CIFOA	AMFOA
F1	Avg	1.30 × 107	1.25 × 106	1.23 × 107	4.81 × 106	5.72 × 109	1.02 × 107	1.85 × 109	1.64 × 1010	1.21 × 1010	1.31 × 1010
	Std	3.36 × 106	5.59 × 105	4.89 × 106	1.75 × 106	1.90 × 109	2.99 × 106	5.26 × 108	7.19 × 108	2.46 × 109	8.28 × 108
	Rank	5	1	4	2	7	3	6	10	8	9
	p-value	-	1.73 × 10−6	3.71 × 10−1	1.73 ×10−6	1.73 × 10−6	2.25 × 10−3	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F2	Avg	4.41 × 103	1.51 × 104	1.87 × 105	1.38 × 105	2.01× 11	3.52× 06	1.25 × 1011	1.99 × 1011	1.91 × 1011	1.89 × 1011
	Std	3.71 × 103	1.12 × 104	9.54 × 105	3.89 × 104	2.85 × 1010	8.38 × 105	1.33 × 1010	5.37 × 108	5.11 × 108	6.09 × 109
	Rank	1	2	4	3	10	5	6	9	8	7
	p-value	-	1.74 ×10−4	4.71 × 10−2	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F3	Avg	3.69 × 104	1.12 × 10−5	8.37 × 103	3.89 × 102	5.33 × 105	3.35 × 103	1.73 × 105	6.81 × 108	1.31 × 107	5.27 × 107
	Std	4.89 × 103	2.36 × 104	8.78 × 103	3.63 × 101	1.83 × 105	1.50 × 103	3.12 × 104	1.95 × 107	2.26 × 107	5.71 × 107
	Rank	4	5	3	1	7	2	6	10	8	9
	p-value	-	1.73 × 10−6	1.92 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F4	Avg	5.28 × 102	5.19 × 102	5.30 × 102	5.16 × 102	6.41 × 104	5.51 × 102	3.16 × 104	7.18 × 104	6.65 × 104	6.02 × 104
	Std	2.91 × 101	3.84 × 101	4.41 × 101	4.58 × 101	1.58 × 104	4.31 × 101	7.29 × 103	7.73 × 102	3.85 × 102	1.95 × 103
	Rank	3	2	4	1	8	5	6	10	9	7
	p-value	-	3.18 × 10−1	8.77 × 10−1	1.30 × 10−1	1.73 × 10−6	2.18 × 10−2	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F5	Avg	5.21 × 102	5.21 × 102	5.20 × 102	5.20 × 102	5.21 × 102	5.21× 102	5.21 × 102	5.22 × 102	5.21 × 102	5.21 × 102
	Std	4.65 × 10−2	2.38 × 10−1	2.30 × 10−1	9.69 × 10−2	4.02 × 10−2	9.07 × 10−2	4.58 × 10−2	4.33 × 10−2	2.94 × 10−2	6.99 × 10−2
	Rank	5	4	2	1	9	3	7	10	6	8
	p-value	-	2.25 × 10−3	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	2.35 × 10−6	1.73 × 10−6
F6	Avg	6.35 × 102	6.65 × 102	6.73 × 102	6.70 × 102	6.80 × 102	6.55 × 102	6.71 × 102	6.90 × 102	6.85 × 102	6.85 × 102
	Std	1.19 × 101	3.32 × 100	4.38 × 100	4.81 × 100	3.63 × 100	4.89 × 100	3.59 × 100	3.78 × 10−1	1.31 × 100	7.42 × 101
	Rank	1	3	6	4	7	2	5	10	8	9
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F7	Avg	7.00 × 102	7.00 × 102	7.00 × 102	7.00 × 102	2.56 × 103	7.01 × 102	1.84 × 103	2.56 × 103	2.49 × 103	2.43 × 103
	Std	3.53 × 10−3	1.09 × 10−2	1.57 × 10−1	5.11 × 10−2	3.60 × 102	1.58 × 10−2	1.35× 102	2.14 × 101	4.91 × 100	1.53 × 101
	Rank	1	2	3	4	9	5	6	10	8	7
	p-value	-	1.6 × 10−4	9.91 × 10−3	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F8	Avg	9.55 × 102	1.30 × 103	1.17 × 103	1.19 × 103	1.60 × 103	9.95 × 102	1.38 × 103	1.69 × 103	1.60 × 103	1.65 × 103
	Std	1.26 × 101	5.35 × 101	6.30 × 101	5.38 × 101	6.30 × 101	3.24 × 101	4.30 × 101	1.59 × 101	6.13 × 100	2.20 × 101
	Rank	1	5	3	4	8	2	6	10	7	9
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.02 × 10−5	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F9	Avg	1.26 × 103	1.61 × 103	1.41 × 103	1.42 × 103	1.84 × 103	1.32 × 103	1.57 × 103	1.88 × 103	1.78 × 103	1.78 × 103
	Std	2.84 × 101	9.97 × 101	8.96 × 101	9.41 × 101	1.02 × 102	7.42 × 101	5.94 × 101	2.15 × 101	7.13 × 100	3.09 × 101
	Rank	1	6	3	4	9	2	5	10	7	8
	p-value	-	1.73 × 10−6	2.35 × 10−6	1.92 × 10−6	1.73 × 10−6	1.18 × 10−3	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F10	Avg	3.62 × 103	8.95 × 103	8.81× 103	8.87 × 103	1.68 × 104	4.81 × 103	1.37 × 104	1.92 × 104	1.69 × 104	1.82 × 104
	Std	2.63 × 102	9.69 × 102	9.68 × 102	1.08 × 103	6.87 × 102	7.58 × 102	7.53 × 102	1.70 × 102	3.12 × 102	4.85 × 102
	Rank	1	5	3	4	7	2	6	10	8	9
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	3.88 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F11	Avg	1.14 × 104	8.54 × 103	8.80 × 103	8.92 × 103	1.70 × 104	8.57 × 103	1.52 × 104	1.91 × 104	1.67 × 104	1.77 × 104
	Std	6.78 × 102	6.41 × 102	9.33 × 102	7.13 × 102	8.18 × 102	9.88 × 102	1.04 × 103	2.33 × 102	1.28 × 102	1.36 × 102
	Rank	5	1	3	4	8	2	6	10	7	9
	p-value	-	1.73 × 10−6	1.92 × 10−6	1.73 × 10−6	1.73 × 10−6	1.92 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F12	Avg	1.20 × 103	1.20 × 103	1.20 × 103	1.20 × 103	1.21 × 103	1.20 × 103	1.20 × 103	1.21 × 103	1.20 × 103	1.21 × 103
	Std	4.15 × 10−1	4.24 × 10−1	6.59 × 10−1	6.04 × 10−1	9.86 × 10−1	4.91 × 10−1	8.92 × 10−1	9.80 × 10−1	2.76 × 10−1	9.65 × 10−1
	Rank	5	1	4	2	9	3	6	10	7	8
	p-value	-	1.73 × 10−6	4.90 × 10−4	2.35 × 10−6	1.73 × 10−6	2.13 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F13	Avg	1.30 × 103	1.30 × 103	1.30 × 103	1.30 × 103	1.31 × 103	1.30 × 103	1.31 × 103	1.31 × 103	1.31 × 103	1.31 × 103
	Std	4.30 × 10−2	9.22 × 10−2	8.32 × 10−2	1.08 × 10−1	9.09 × 10−1	1.08 × 10−1	5.31 × 10−1	1.25 × 10−2	1.48 × 10−2	7.65 × 10−2
	Rank	3	1	2	4	9	5	6	10	8	7
	p-value	-	2.37 × 10−1	2.29 × 10−1	6.00 × 10−1	1.73 × 10−6	3.16 × 10−2	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F14	Avg	1.40 × 103	1.40 × 103	1.40 × 103	1.40 × 103	1.83 × 103	1.40 × 103	1.65 × 103	1.87 × 103	1.86 × 103	1.82 × 103
	Std	3.13 × 10−2	6.86 × 10−2	1.13 × 10−1	1.13 × 10−1	5.66 × 101	1.93 × 10−1	2.58 × 101	5.45 × 100	1.46 × 100	1.38 × 101
	Rank	1	4	2	3	8	5	6	10	9	7
	p-value	-	3.38 × 10−3	1.78 × 10−1	3.68 × 10−2	1.73 × 10−6	8.94 × 10−4	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F15	Avg	1.53 × 103	2.04 × 103	1.63 × 103	1.58 × 103	4.03 × 107	1.55 × 103	3.66 × 106	2.54 × 107	1.59 × 107	7.64 × 106
	Std	2.08 × 100	1.49 × 102	3.91× 101	2.18× 101	3.26 × 107	1.09 × 101	1.87 × 106	1.19 × 106	5.14 × 105	2.07 × 106
	Rank	1	5	4	3	10	2	6	9	8	7
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	2.35 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F16	Avg	1.62 × 103	1.62 × 103	1.62 × 103	1.62 × 103	1.62 × 103	1.62 × 103	1.62 × 103	1.62 × 103	1.62 × 103	1.62 × 103
	Std	3.17 × 10−1	4.08 × 10−1	4.78 × 10−1	4.66 × 10−1	2.09 × 10−1	6.33 × 10−1	3.88 × 10−1	1.80 × 10−1	6.98 × 10−2	1.80 × 10−1
	Rank	1	5	7	4	9	2	3	10	6	8
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	2.30 × 10−2	2.35 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F17	Avg	1.54 × 106	7.30 × 104	9.46 × 105	5.26 × 105	9.85 × 108	1.67 × 106	5.08 × 108	3.87 × 109	1.98 × 109	1.88 × 109
	Std	8.74 × 105	3.66 × 104	4.18 × 105	2.53 × 105	4.56 × 108	7.03 × 105	2.87 × 108	1.97 × 107	7.28 × 108	4.50 × 108
	Rank	4	1	3	2	7	5	6	10	9	8
	p-value	-	1.73 × 10−6	1.04 × 10−3	2.35 × 10−6	1.73 × 10−6	3.82 × 10−1	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F18	Avg	3.54 × 103	5.03 × 103	4.57 × 103	5.52 × 103	2.09 × 1010	2.84 × 104	6.75 × 109	3.78 × 1010	3.45 × 1010	3.14 × 1010
	Std	1.03 × 103	1.44 × 103	2.11 × 103	1.87 × 103	5.86 × 109	1.57 × 104	2.90 × 109	3.15 × 108	2.44 × 109	2.13 × 109
	Rank	1	3	2	4	7	5	6	10	9	8
	p-value	-	3.59 × 10−4	2.85 × 10−2	9.71 × 10−5	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F19	Avg	1.95 × 103	1.99 × 103	1.96 × 103	1.96 × 103	5.04 × 103	1.95 × 103	2.94 × 103	1.08 × 104	9.08 × 103	8.12 × 103
	Std	3.14 × 101	2.77 × 101	2.58 × 101	2.85 × 101	1.53 × 103	2.84 × 101	2.73 × 102	1.23 × 102	7.93 × 102	6.17 × 102
	Rank	1	5	3	4	7	2	6	10	9	8
	p-value	-	2.84 × 10−5	7.03 × 10−1	2.71 × 10−1	1.73 × 10−6	7.81 × 10−1	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F20	Avg	1.13 × 104	4.43 × 104	4.24 × 103	2.82 × 103	9.50 × 106	8.83 × 103	6.70 × 105	3.22 × 109	7.50 × 107	2.69 × 109
	Std	2.99 × 103	1.83 × 104	3.14 × 103	1.52 × 102	7.96 × 106	5.66 × 103	8.59 × 105	0.00 × 100	4.87 × 107	9.58 × 108
	Rank	4	5	2	1	7	3	6	10	8	9
	p-value	-	1.73 × 10−6	8.47 × 10−6	1.73 × 10−6	1.73 × 10−6	3.68 × 10−2	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F21	Avg	1.67 × 106	8.75 × 104	5.42 × 105	3.43 × 105	2.19 × 108	8.61 × 105	8.04 × 107	1.80 × 109	8.18 × 108	4.95 × 108
	Std	4.61 × 105	3.81 × 104	2.70 × 105	1.79 × 105	1.04 × 108	4.24 × 105	4.69 × 107	3.19 × 107	3.40 × 108	1.83 × 108
	Rank	5	1	3	2	7	4	6	10	9	8
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.36 × 10−5	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F22	Avg	3.13 × 103	4.09 × 103	4.26 × 103	4.19 × 103	3.27 × 105	3.93 × 103	1.91 × 104	6.11 × 106	1.89 × 106	4.64 × 106
	Std	2.26 × 102	3.71 × 102	3.50 × 102	4.44 × 102	5.28 × 105	3.76 × 102	2.20 × 104	2.01 × 104	1.45 × 106	6.69 × 105
	Rank	1	3	5	4	7	2	6	10	8	9
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.92 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F23	Avg	2.63 × 103	2.65 × 103	2.65 × 103	2.64 × 103	4.89 × 103	2.64 × 103	3.11 × 103	2.50 × 103	2.50 × 103	2.50 × 103
	Std	4.39 × 101	3.11 × 100	2.16 × 100	2.12 × 10−1	6.99 × 102	2.96 × 10−1	5.70 × 102	0.00 × 100	4.05 × 10−1	5.09 × 10−4
	Rank	4	7	8	5	10	6	9	1	3	2
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	3.61 × 10−3	1.73 × 10−6	1.73 × 10−6	3.18 × 10−6
F24	Avg	2.60 × 103	2.79 × 103	2.77 × 103	2.76 × 103	3.07 × 103	2.62 × 103	2.60 × 103	2.60 × 103	2.60 × 103	2.60 × 103
	Std	1.14 × 10−8	8.48 × 101	5.14 × 101	5.89 × 101	6.62 × 101	2.11 × 101	7.38 × 10−1	0.00 × 100	1.21 × 10−1	2.82 × 10−1
	Rank	2	9	8	7	10	6	5	1	3	4
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	3.11 × 10−5	1.73 × 10−6
F25	Avg	2.70 × 103	2.75 × 103	2.76 × 103	2.76 × 103	3.00 × 103	2.72 × 103	2.70 × 103	2.70 × 103	2.70 × 103	2.70 × 103
	Std	0.00 × 100	1.84 × 101	2.67 × 101	2.14 × 101	8.62 × 101	2.48 × 101	0.00 × 100	0.00 × 100	0.00 × 100	1.41 × 10−5
	Rank	1	7	9	8	10	6	1	1	1	5
	p-value	-	1.73 × 10-6	1.73 × 10-6	1.73 × 10-6	1.73 × 10-6	1.73 × 10-6	1.00 × 100	1.00 × 100	1.00 × 100	1.73 × 10-6
F26	Avg	2.76 × 103	2.75 × 103	2.73× 03	2.80 × 103	2.91 × 103	2.70 × 103	2.77 × 103	2.80 × 103	2.80 × 103	2.80 × 103
	Std	5.00 × 101	1.18 × 102	1.02 × 102	1.43 × 102	1.96 × 102	1.82 × 101	4.16 × 101	0.00 × 100	0.00 × 100	7.13 × 10-8
	Rank	4	3	2	9	10	1	5	6	6	8
	p-value	-	4.78 × 10−1	4.95 × 10−2	1.98 × 10−1	1.28 × 10−3	7.16 × 10−4	2.78 × 10−2	2.44 × 10−4	2.44 × 10−4	1.73 × 10−6
F27	Avg	3.13 × 103	4.89 × 103	5.04 × 103	4.98 × 103	5.55 × 103	4.48 × 103	5.01 × 103	2.90 × 103	2.90 × 103	2.90 × 103
	Std	5.64 × 101	1.26 × 102	3.82 × 102	3.88 × 102	2.81 × 102	2.98 × 102	1.34 × 102	1.39 × 10−12	1.39 × 10−12	7.74 × 10−5
	Rank	4	6	9	7	10	5	8	1	1	3
	p-value	-	1.73 × 10−6	1.92 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F28	Avg	3.99 × 103	8.63 × 103	8.77 × 103	9.10 × 103	1.56 × 104	7.03 × 103	8.46 × 103	3.00 × 103	3.00 × 103	3.00 × 103
	Std	7.15 × 101	1.77 × 103	1.75 × 103	1.66 × 103	2.30 × 103	1.06 × 103	4.44 × 103	1.39 × 10−12	3.10 × 10−1	8.84 × 10−4
	Rank	4	7	8	9	10	5	6	1	3	2
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	6.16 × 10−4	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6
F29	Avg	5.34 × 103	1.49 × 108	4.27 × 108	1.73 × 108	8.94 × 108	2.16 × 107	2.25 × 108	3.10 × 103	1.68 × 105	7.96 × 103
	Std	5.24 × 102	1.20 × 108	2.17 × 108	1.10 × 108	3.63 × 108	2.08 × 107	1.94 × 108	0.00 × 100	9.01 × 105	1.05 × 103
	Rank	2	6	9	7	10	5	8	1	4	3
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	5.31 × 10−5	1.73 × 10−6	3.11 × 10−5	1.73 × 10−6
F30	Avg	1.41 × 104	2.32 × 105	4.93 × 105	3.12 × 104	3.35 × 107	2.34 × 104	7.34 × 106	3.20 × 103	5.60 × 103	3.44 × 103
	Std	1.71 × 103	5.90 × 105	1.55 × 106	7.14 × 103	1.68 × 107	4.07 × 103	3.89 × 106	0.00 × 100	1.32 × 104	6.38 × 101
	Rank	4	7	8	6	10	5	9	1	3	2
	p-value	-	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	1.73 × 10−6	3.11 × 10−5	1.73 × 10−6

shows the average fitness value and standard deviation of each algorithm on the 30 benchmark function test sets. It can be seen that the performance of RCCBOA on some test functions is better than that of other algorithms. It is proven that the proposed algorithm has significant advantages compared with other algorithms on the IEEE CEC2014 test set. First, the average result (Avg) and standard deviation (Std) of the optimization values were used to evaluate the potential of the relevant optimizer. Furthermore, we employed the Wilcoxon signed-rank test to evaluate whether the performance of RCCBOA was significantly better than that of other state-of-the-art algorithms in this experiment. It can be seen that the p-values calculated on most test functions were all lower than 0.05, indicating that the RCCBOA had a good performance on most benchmark functions. Furthermore, we screened nine representative convergence plots on the IEEE CEC2014 test benchmark function, as shown in Figure 4. It can be seen that the RCCBOA had an excellent convergence speed and convergence value on nine test functions.

In order to further study the effect of random replacement and the crisscross search mechanism on the computation time of BOA, computation time experiments were conducted under the same environment. The experimental results are shown in Figure 5. It can be seen that, compared with the original BOA, the calculation time of RCCBOA was greatly improved in the IEEE CEC2014 benchmark test set. Overall, MWOA was the most time-consuming to calculate, followed by RCCBOA. In addition, the times taken by CDLOBA, CBA, RCBA, LWOA, IWOA, CEFOA, CIFOA, and AMFOA were very close. In conclusion, the introduction of the two mechanisms effectively improved the performance of the BOA as well as improving the execution time. Therefore, when solving practical problems, there is a trade-off between performance and time consumption.

6.2. Research of Overseas Chinese Associations

In this section, we describe ten independent experimental evaluations of the RCCBOA-SVM (RCCBOA-SVM-FS) model with feature selection, the detailed results of which are shown in

Table 7. Classification results obtained for RCCBOA-SVM-FS with four metrics.

Fold	Accuracy	Sensitivity	Specificity	MCC
Num.1	0.94	1.00	0.89	0.89
Num.2	0.91	1.00	0.82	0.84
Num.3	0.99	1.00	0.97	0.97
Num.4	0.96	0.96	0.93	0.91
Num.5	0.96	0.97	0.94	0.91
Num.6	0.94	0.97	0.90	0.88
Num.7	0.93	1.00	0.86	0.86
Num.8	0.96	1.00	0.92	0.91
Num.9	0.96	1.00	0.92	0.91
Num.10	0.94	1.00	0.97	0.88
Avg	0.95	0.99	0.91	0.90
Std	0.02	0.02	0.04	0.03

. It can easily be seen that the average accuracy obtained using RCCBOA-SVM-FS was 95%, the sensitivity was 99%, the specificity was 91%, and the MCC index was 90%, with mean standard deviations of 0.02, 0.02, 0.04, and 0.03. Furthermore, the optimal parameters and feature subsets in this experiment were obtained directly through the RCCBOA method, indicating that the constructed model was helpful for guiding the orderly and healthy development of overseas Chinese groups.

To further verify the performance of the algorithm, we conducted comparative experiments with another five machine learning models, RCCBOA-SVM, BOA-SVM, ANN, RF, and KELM; the detailed results are shown in Figure 6. The experimental results show that RCCBOA-SVM-FS was better than RCCBOA-SVM, ANN, RF, and KELM in all four evaluation metrics. For the accuracy rate, RCCBOA-SVM-FS had an accuracy rate of about 95%, while the accuracy rates of the other five comparison models were 93%, 91%, 87%, 93%, and 91%, respectively. Regarding the sensitivity index, both RCCBOA-SVM-FS and KELM had values of 99%, 0.06% higher than the that of the lowest ANN. For the specificity index, RCCBOA-SVM-FS, RCCBOA-SVM, and RF surpassed the proportion of 91%. The specificity values of RBOA-SVM, ANN, and KELM were 83%, 80%, and 83%, respectively. In terms of the MCC indicator, RCCBOA-SVM-FS performed the best, with a value of up to 90%. The worst performer was ANN, with a value of 73%. In short, from the above four indicators, it can be seen that the performance of RCCBOA-SVM-FS was better than that of the other five models, and the model accuracy rate was as high as 95%. Therefore, RCCBOA-SVM-FS was effective and reliable for constructing a standardized construction model of overseas Chinese communities.

Moreover, the proposed RCCBOA obtained the optimal settings of the SVM hyperparameters as well as the optimal feature set. Here, we used the 10-fold cross-validation technique combined with the RCCBOA algorithm to identify features that have an important impact on the normalization of overseas Chinese groups. Figure 7 illustrates the frequencies of dominant features identified by RCCBOA-SVM-FS via 10-fold cross-validation.

As shown in Figure 7, whether the charter of the overseas Chinese association is reasonable (A22), whether the overseas Chinese association holds regular meetings (A23), and whether every member of the association has the right to vote and be elected (A24) were the top three features in terms of frequency, appearing 9, 8, and 9 times, respectively. Therefore, it can be concluded that these characteristics may play an important role in the standardized construction of overseas Chinese groups.

7. Discussion

The normative nature of overseas Chinese associations is subject to various conditions. Based on the data of overseas Chinese associations, this paper obtained the most important features and models by combining the support vector machine model with RCCBOA. The RCCBOA was introduced and compared with advanced algorithms. It can be seen that when solving related benchmark problems, it had a strong performance. The performance of SVM models can easily be affected by hyperparameters. Therefore, the RCCBOA was combined with SVM and used to extract important features and obtain the best model. From the experimental results found in the study, it can be seen that three attributes—namely, attributes A22, A23, and A24—made up the most important characteristics of overseas Chinese associations, having prominent impacts on the standardized construction of overseas Chinese associations. Generally speaking, an overseas Chinese association which formulates reasonable policies; holds regular meetings; and grants every member of the association the right to vote, stand for election, and vote is standardized. Taking these three features as the main reference attributes, combined with other attributes, a fast judgement of the formality and regularity of an overseas Chinese association can be made using computer algorithm calculation. The advantage of the proposed RCCBOA method is that it can fully mine the key features of data. Based on this advantage, this method also has potential applications in other problems, such as kayak cycle phase segmentation [105], recommender systems [106,107,108,109], text clustering [110], human motion capture [111], energy storage planning and scheduling [112], urban road planning [113], microgrid planning [114], active surveillance [115], image super resolution [116,117], anomaly behavior detection [118], and multivariate time series analysis [119].

This study still has several limitations that need to be further discussed. First of all, the samples used in this study were limited; in order to obtain more accurate results, more continuous samples need to be collected to train a more unbiased learning model. Secondly, this study mainly focused on overseas Chinese associations composed of Zhejiang nationals, most of whom were Chinese citizens newly overseas and living mostly in Europe and the United States; therefore, the research data obtained for global overseas Chinese associations were not sufficient and had regional limitations. The determination of the model used in multicenter research made the model more reliable for decision support. In addition, the attributes involved in the study were limited, and future research should seek to use more attributes that have an impact on the standardization construction of overseas Chinese associations.

8. Conclusions and Future Work

In this paper, an improved BOA algorithm combining random replacement and crisscross search is proposed to study the normalized construction of overseas Chinese groups. The main innovation of the proposed RCCBOA is the introduction of two mechanisms, which effectively improves the convergence speed and convergence accuracy of the original BOA. The comparison experiments performed with other nine advanced algorithms on the CEC2014 benchmark function test set show that the RCCBOA can obtain better solutions and a better stability. Further, the RCCBOA is combined with SVM for better hyperparameter combinations and feature subsets. From the experimental results, it can be seen that the features of A22, A23 and A24 are of great significance to its planning and standardized construction. Compared with other machine learning methods, the proposed method is 95% accurate when dealing with the normative prediction problem of overseas Chinese citizens.

In follow-up studies, the RCCBOA-SVM-FS model will be applied to other problems, such as disease diagnosis and bankruptcy prediction. Of course, it is expected that the proposed RCCBOA can be extended to solve optimization problems in other fields, such as photovoltaic cell parameter identification and image segmentation.